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Unformatted text preview: : Time for the mole fraction of A in the instantaneous distillate to fall to 0.40.
Analysis: Base the calculations on A, which is the more volatile component. Initially, the
distillate mole fraction in equilibrium with the initial charge is obtained from Eq. (4-8) for
constant relative volatility, α:
1 + x (α − 1) 1 + 0.30(2.5 − 1) (1) When the mole fraction of A in the instantaneous distillate = yD = 0.40, the mole fraction of A in
the liquid in the still is obtained form a rearrangement of Eq. (1),
α + y (1 − α ) 2.5 + 0.40(1 − 2.5) Modify Eq. (13-1) to include the constant feed added to the still, noting that, with the above
assumptions, W = total moles in the still = constant = W0 = 20 lbmole, dW/dt = 0, and the
distillate rate, call it D = molar feed rate, F:
Fx F − W dx
= Dy D = Fy D
dt Rearranging, dx F x F − y D
W0 (2) Eq. (2) is integrated as follows, noting that yD = y. Substituting Eq. (1) into Eq. (2) gives,
t 0.2105 0 0.305 0.5 dt = 0.50t = dx
(1 + 15x )dx
0.30 − 2.05x
1 + x (α − 1)
1 + 15x
. 1 + 15x )dx
0.305 − 2.05x Therefore, t = 0.585/0.5 = 1.17 h Exercise 13.9
Subject: Batch distillation of a mixture of isopropyl alcohol (P) and water (W) in a column with
2 equilibrium stages and a reboiler, under conditions of a constant reflux ratio.
Given: Feed contains 40 mol% P and 60 mol% W. Distillation at 1 atm with a reflux of L/V =
0.9. Vapor-liquid equilibrium data in Exercise 13.2.
Assumptions: Perfect mixing in the still. No holdup on the stages or in the condenser.
Find: Compositions of the residue in the still and cumulative distillate when 70 mol% of the
charge has been distilled (W/W0 = 0.30).
Analysis: Make calculations in terms of P, the more volatile component. Eq. (13-2) applies,
where yD is the mole fraction of P in the vapor leaving the top stage, and xW is the mole fraction
of P in the liquid in the reboiler. ln W0
= 1.204 =
y D − xW (1) The relationship between yD and xW is obtained from a McCabe-Thiele diagram by drawing a
series of operating lines of slope = L/V = 0.9. For each operating line, starting from the
intersection with the 45o line, which is yD, 3 stages are stepped off to determine the
corresponding xW. A typical construction that starts from yD = 0.65 is shown on the next page,
where the xW = 0.37. Other sets of values are given in the following table, which also includes
values of the integrand, f = 1/(yD - xW), from which the integral is evaluated by the trapezoidal
rule with variable increments of ∆xW. For example, the increment of the integral from x1 to x2 is
(x1 - x2)(f1/2 + f2/2).
The increments are summed over the region from xW = 0.40 to the value corresponding to 70
mol% distilled. xW yD from
McCabe-Thiele f = 1/(yD - xW) 0.400
2.01 Increment of
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This document was uploaded on 02/24/2014 for the course CBE 2124 at NYU Poly.
- Spring '11
- The Land